Raymond Viglione

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Let q be a prime power and k ≥ 2 be an integer. In [2] and [3] it was determined that the number of components of certain graphs D(k, q) introduced in [1] is at least qt−1 where t = b k+2 4 c. This implied that these components (most often) provide the best-known asymptotic lower bound for the greatest number of edges in graphs of their order and girth. In(More)
Let q be a prime power, Fq be the field of q elements, and k;m be positive integers. A bipartite graph G 1⁄4 Gqðk;mÞ is defined as follows. The vertex set of G is a union of two copies P and L of two-dimensional vector spaces over Fq, with two vertices ðp1;p2Þ 2 P and 1⁄2 l1; l2 2 L being adjacent if and only if p2 þ l2 1⁄4 p 1 l 1 . We prove that graphs(More)
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